Artificial Viscosity Discontinuous Galerkin Spectral Element Method for the Baer-Nunziato Equations

This paper is devoted to the numerical discretization of the hyperbolic two-phase flow model of Baer and Nunziato. Special attention is paid to the discretization of interface flux functions in the framework of Discontinuous Galerkin approach, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. A discretization scheme is proposed in a Discontinuous Galerkin framework following the criterion of Abgrall. A stabilization technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and tested on a bench of discontinuous test cases.